The tracing of dye injections constitutes a fluid visualization technique for the tracking of flows. Dye experimentation is widely used in experimental fluid mechanics for flow analysis or for the study of the transport of particles within a fluid [1]}. Such a method is particularly useful in biomedical diagnostic applications ranging from blood flow analysis in the cardiovascular system to ocular circulation. Although dye tracing is most commonly known as an experimental approach, it can also serve as a useful post-processing analysis tool in computational fluid dynamics (CFD) studies [2]}. Numerical dye studies can facilitate the identification of the relative significance of spatial subregions within particular time intervals of an unsteady flow field. For example, dye simulations can be applied to the aorta in order to visualize the time histories of the effects of the pulsatile velocity fields on injected medication as well as to investigate the effects of previous cardiac cycles on the distribution of a drug [3]}, [4]}, [2]}. Mathematically speaking, dye simulations are also related to particle residence time (PRT) calculations, both of which can be formulated as convection-diffusion problems [6]}, [7]}, [2]}. PRT is an important metric for a variety of applications including those found in environmental fluid dynamics [9]}, [10]}, biological flows [11]}, and hemodynamics [12]}, [13]}, [14]}. In particular, PRT is now a well-accepted biomarker for cardiovascular diseases (e.g., stroke, myocardial infarction and embolism) since it is inextricably linked to thrombus (blood clot) formation [15]}, [16]}, [17]}, [18]}, [3]}.
